I am creating composites of a host epoxy and filler particles which are thin-walled fluid-filled shells. Using the Halpin-Tsai equations, for example, I can predict the bulk composite Young's modulus by knowing the particle volume fraction, modulus, geometry, etc, and this seems to work well for both Solid and Liquid particles (using a negligible modulus to approximate liquid)
However, I am having difficulty determining the effective modulus of a liquid-core shell particle for use in these equations. I have found this paper Bulk Modulus of a fluid-filled spherical shell which provides a formula to predict the Bulk Modulus of such a shell, but without also knowing the Shear Modulus or Poisson's Ratio of these fluid-filled shells I cannot determine a Young's Modulus.
This seems like something that should have a well-documented formula, but I can't seem to find anything. Any ideas on how to calculate the Young's Modulus?